Composite operator approach to dynamical mass generation in the (2+1)-dimensional Gross-Neveu model

TL;DR

This paper uses a nonperturbative CJT effective action approach to analyze the phase structure of the massless (2+1)-dimensional Gross-Neveu model, revealing three possible dynamical fermion masses and phases.

Contribution

It introduces a first-order calculation of the CJT effective action in the Gross-Neveu model, identifying three distinct dynamical mass generation scenarios.

Findings

Three different fermion masses can be generated dynamically.

The phase structure depends on the cutoff parameter and coupling constant.

Three nontrivial phases are identified in the model.

Abstract

Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis (CJT) effective action $\Gamma(S)$ for composite operators, the phase structure of the simplest massless (2 + 1)-dimensional Gross-Neveu model is investigated. We have calculated $\Gamma(S)$ in the first order of the bare coupling constant $G$ and have shown that there exist three different specific dependences of $G\equiv G(\Lambda)$ on the cutoff parameter $\Lambda$, and in each case the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.